#486 ⟨a, b | aabb=1, baba=1⟩

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Properties

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. ba ⇒ ab
  2. a2b2 ⇒ 1 
# ab:aabb=1,baba=1 ab
ba=ab
aabb=1

Staircase diagram

Right Cayley graph (truncated)

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

28 total

Σ#PresentationMapping
8488⟨a, b | abab=1, abba=1⟩φ(a) = a, φ(b) = b
8621⟨a, b | ba=ab, aabb=1⟩φ(a) = a, φ(b) = b
8622⟨a, b | ba=ab, abab=1⟩φ(a) = a, φ(b) = b
8623⟨a, b | ba=ab, abba=1⟩φ(a) = a, φ(b) = b
104028⟨a, b | aba=aab, abba=1⟩φ(a) = a, φ(b) = b
104031⟨a, b | aba=aab, baab=1⟩φ(a) = a, φ(b) = b
104032⟨a, b | aba=aab, baba=1⟩φ(a) = a, φ(b) = b
104034⟨a, b | aba=aab, bbaa=1⟩φ(a) = a, φ(b) = b
105885⟨a, b | aabb=1, abbba=b⟩φ(a) = a, φ(b) = b
105890⟨a, b | aabb=1, babaa=a⟩φ(a) = a, φ(b) = b
105914⟨a, b | abab=1, abbaa=a⟩φ(a) = a, φ(b) = b
105920⟨a, b | abab=1, baaba=a⟩φ(a) = a, φ(b) = b
105924⟨a, b | abab=1, bbaaa=a⟩φ(a) = a, φ(b) = b
105936⟨a, b | abba=1, aabab=a⟩φ(a) = a, φ(b) = b
105944⟨a, b | abba=1, ababa=a⟩φ(a) = a, φ(b) = b
105947⟨a, b | abba=1, ababb=b⟩φ(a) = a, φ(b) = b
105951⟨a, b | abba=1, abbba=b⟩φ(a) = a, φ(b) = b
105954⟨a, b | abba=1, baaab=a⟩φ(a) = a, φ(b) = b
105959⟨a, b | abba=1, babab=b⟩φ(a) = a, φ(b) = b
106913⟨a, b | ba=ab, aaaabb=1⟩φ(a) = b, φ(b) = aaab
106915⟨a, b | ba=ab, aaabab=1⟩φ(a) = b, φ(b) = aaab
106916⟨a, b | ba=ab, aaabba=1⟩φ(a) = b, φ(b) = aaab
106918⟨a, b | ba=ab, aabaab=1⟩φ(a) = b, φ(b) = aaab
106919⟨a, b | ba=ab, aababa=1⟩φ(a) = b, φ(b) = aaab
106921⟨a, b | ba=ab, aabbaa=1⟩φ(a) = b, φ(b) = aaab
106924⟨a, b | ba=ab, abaaab=1⟩φ(a) = b, φ(b) = aaab
106925⟨a, b | ba=ab, abaaba=1⟩φ(a) = b, φ(b) = aaab
106929⟨a, b | ba=ab, abbbba=1⟩φ(a) = aaab, φ(b) = b